Substitution D.E

Ok, so i do everything to one point and can't get the right answer.
The question is:

By using the substitution y = xu solve:

The answer is:

Now, i differentiate y = xu:
After substituting in and canceling i get:
I then take u to the otherside and put it into the fraction, multiply and integrate to get:
Taking the exponential:
Then i substitute in y = xu ( u = y / x) :
Re-arranging:
Making y the subject does not give the anwser.